Elliptic curve isogeny class 3750.1-f over number field \(\Q(\sqrt{3}) \)

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-3750.1-f
• Conductor: 3750.1
• Rank: \( 0 \)

Base field \(\Q(\sqrt{3}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 3 \); class number \(1\).

Elliptic curves in class 3750.1-f over \(\Q(\sqrt{3}) \)

Isogeny class 3750.1-f contains 4 curves linked by isogenies of degrees dividing 10.

Curve label	Weierstrass Coefficients
3750.1-f1	\( \bigl[a\) , \( 1\) , \( a\) , \( -76\) , \( 299\bigr] \)
3750.1-f2	\( \bigl[1\) , \( -a\) , \( 1\) , \( 39229 a - 67950\) , \( 26773532 a - 46373129\bigr] \)
3750.1-f3	\( \bigl[1\) , \( -a\) , \( 1\) , \( 1159229 a - 2007950\) , \( 892013532 a - 1545013129\bigr] \)
3750.1-f4	\( \bigl[a\) , \( 1\) , \( a\) , \( -1326\) , \( 17799\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 5 & 10 & 2 \\ 5 & 1 & 2 & 10 \\ 10 & 2 & 1 & 5 \\ 2 & 10 & 5 & 1 \end{array}\right)\)

Isogeny graph